TSTP Solution File: SCT203_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT203_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:51:15 EDT 2023
% Result : Theorem 262.43s 205.51s
% Output : Refutation 263.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 166
% Syntax : Number of formulae : 286 ( 75 unt; 48 typ; 0 def)
% Number of atoms : 4403 ( 202 equ; 0 cnn)
% Maximal formula atoms : 298 ( 18 avg)
% Number of connectives : 16218 ( 133 ~; 21 |; 77 &;15711 @)
% ( 33 <=>; 243 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 13 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 47 usr; 16 con; 0-6 aty)
% Number of variables : 948 ( 0 ^; 885 !; 21 ?; 948 :)
% ( 42 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(arrow_159774573e_indi_type,type,
arrow_159774573e_indi: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(top_type,type,
top:
!>[TA: $tType] : $o ).
thf(arrow_1958449194le_IIA_type,type,
arrow_1958449194le_IIA: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(arrow_1985332922le_Lin_type,type,
arrow_1985332922le_Lin: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ).
thf(arrow_610318064e_Prof_type,type,
arrow_610318064e_Prof: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ).
thf(arrow_1158827142_above_type,type,
arrow_1158827142_above: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_319942042_below_type,type,
arrow_319942042_below: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_987702531ctator_type,type,
arrow_987702531ctator: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > arrow_159774573e_indi > $o ).
thf(arrow_276188178_mkbot_type,type,
arrow_276188178_mkbot: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_424895264_mktop_type,type,
arrow_424895264_mktop: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_2069624013nimity_type,type,
arrow_2069624013nimity: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ TB @ ( fun @ TC @ TA ) ) ) ).
thf(combi_type,type,
combi:
!>[TA: $tType] : ( fun @ TA @ TA ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(pi_type,type,
pi:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TB @ ( fun @ TA @ bool ) ) > ( fun @ ( fun @ TB @ TA ) @ bool ) ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(order_215145569der_on_type,type,
order_215145569der_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(conversep_type,type,
conversep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ bool ) ) > ( fun @ TA @ ( fun @ TB @ bool ) ) ) ).
thf(inv_imagep_type,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ bool ) ) > ( fun @ TA @ TB ) > TA > TA > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( fun @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) ) ).
thf(product_curry_type,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ ( product_prod @ TC @ TB ) @ TA ) > TC > TB > TA ) ).
thf(produc1605651328_split_type,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(converse_type,type,
converse:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > ( fun @ ( product_prod @ TA @ TB ) @ bool ) ) ).
thf(inv_image_type,type,
inv_image:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TB ) @ bool ) > ( fun @ TA @ TB ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).
thf(irrefl_type,type,
irrefl:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(total_on_type,type,
total_on:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(f_type,type,
f: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(p_type,type,
p: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(p1_type,type,
p1: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(q_type,type,
q: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(a_type,type,
a: arrow_411405190le_alt ).
thf(a1_type,type,
a1: arrow_411405190le_alt ).
thf(b_type,type,
b: arrow_411405190le_alt ).
thf(b1_type,type,
b1: arrow_411405190le_alt ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_conversepD) ).
thf(518,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( converse @ TA @ TA @ ( inv_image @ TB @ TA @ B @ A ) )
= ( inv_image @ TB @ TA @ ( converse @ TB @ TB @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_converse__inv__image) ).
thf(142,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
( ( converse @ TA @ TA @ ( inv_image @ TB @ TA @ B @ A ) )
= ( inv_image @ TB @ TA @ ( converse @ TB @ TB @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_mkbot__Lin) ).
thf(248,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(111,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_2069624013nimity @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_unanimity__def) ).
thf(577,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_2069624013nimity @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ C ) @ D ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) )
=> ( arrow_2069624013nimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(21,axiom,
top @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(170,plain,
top @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(94,axiom,
( arrow_1985332922le_Lin
= ( collect @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Lin__def) ).
thf(523,plain,
( arrow_1985332922le_Lin
= ( collect @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( order_215145569der_on @ arrow_411405190le_alt @ ( top_top @ ( fun @ arrow_411405190le_alt @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Pair__eq) ).
thf(276,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(70,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Collect__empty__eq) ).
thf(449,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1,conjecture,
pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ q ) ) @ arrow_1985332922le_Lin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ q ) ) @ arrow_1985332922le_Lin ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(120,plain,
~ ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ q ) ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_prod_Oexhaust) ).
thf(174,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ p ) @ arrow_610318064e_Prof ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096P_H_A_058_AProf_096) ).
thf(185,plain,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ p ) @ arrow_610318064e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
<=> ? [D: TB,E: TA] :
( ( B = E )
& ( A = D )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_conversep_Osimps) ).
thf(504,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
=> ? [D: TB,E: TA] :
( ( B = E )
& ( A = D )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ D ) @ E ) ) ) )
& ( ? [D: TB,E: TA] :
( ( B = E )
& ( A = D )
& ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ D ) @ E ) ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(15,axiom,
a1 != b1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_d1_I1_J) ).
thf(157,plain,
a1 != b1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_prod__induct3) ).
thf(559,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(119,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( total_on @ TA @ B @ A )
<=> ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( ( C != D )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) ) @ A ) )
| ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_total__on__def) ).
thf(606,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( total_on @ TA @ B @ A )
=> ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( ( C != D )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) ) @ A ) )
| ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) ) @ A ) ) ) ) ) ) )
& ( ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( ( C != D )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) ) @ A ) )
| ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) ) @ A ) ) ) ) ) )
=> ( total_on @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ! [C: TA,D: TB] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_pred__equals__eq2) ).
thf(284,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ! [C: TA,D: TB] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(53,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(316,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ D ) @ ( pi @ TA @ TB @ C @ B ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Pi__mem) ).
thf(164,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ D ) @ ( pi @ TA @ TB @ C @ B ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ B @ D ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Pi__I_H) ).
thf(179,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ B @ D ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TB,C: TA] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ B ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) @ ( converse @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_converseI) ).
thf(321,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TB,C: TA] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ B ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) @ ( converse @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(39,axiom,
! [A: arrow_159774573e_indi] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a1 ) @ b1 ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__C1_C) ).
thf(253,plain,
! [A: arrow_159774573e_indi] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a1 ) @ b1 ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a ) @ b ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a1 ) @ b1 ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ TC @ A @ B @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_curry__def) ).
thf(238,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ TC @ A @ B @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(121,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(81,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TA @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TA @ ( combb @ bool @ bool @ TA @ fNot ) ) @ ( fequal @ TA ) ) ) @ A ) @ B ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_conversep__noteq) ).
thf(480,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TA @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TA @ ( combb @ bool @ bool @ TA @ fNot ) ) @ ( fequal @ TA ) ) ) @ A ) @ B ) )
=> ( A != B ) )
& ( ( A != B )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TA @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TA @ ( combb @ bool @ bool @ TA @ fNot ) ) @ ( fequal @ TA ) ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TA,C: TB] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) ) @ ( converse @ TA @ TB @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_converse__iff) ).
thf(602,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TA,C: TB] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) ) @ ( converse @ TA @ TB @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ C ) ) @ A ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ C ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) ) @ ( converse @ TA @ TB @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(7,axiom,
a1 != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_d2_I1_J) ).
thf(133,plain,
a1 != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( produc1605651328_split @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_internal__split__conv) ).
thf(411,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( produc1605651328_split @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TA,C: TB] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) ) @ ( converse @ TA @ TB @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_converseD) ).
thf(243,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TA,C: TB] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) ) @ ( converse @ TA @ TB @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(51,axiom,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ p1 ) @ arrow_610318064e_Prof ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096P_A_058_AProf_096) ).
thf(312,plain,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ p1 ) @ arrow_610318064e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool )] :
( ( pi @ TA @ TB @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
= ( top_top @ ( fun @ ( fun @ TA @ TB ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Pi__empty) ).
thf(260,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool )] :
( ( pi @ TA @ TB @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
= ( top_top @ ( fun @ ( fun @ TA @ TB ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(16,axiom,
! [TA: $tType] :
( ( conversep @ TA @ TA @ ( fequal @ TA ) )
= ( fequal @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_conversep__eq) ).
thf(160,plain,
! [TA: $tType] :
( ( conversep @ TA @ TA @ ( fequal @ TA ) )
= ( fequal @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(105,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_1158827142_above @ A @ C @ B ) ) @ arrow_1985332922le_Lin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_above__Lin) ).
thf(561,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_1158827142_above @ A @ C @ B ) ) @ arrow_1985332922le_Lin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(66,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_319942042_below @ A @ C @ B ) ) @ arrow_1985332922le_Lin ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_below__Lin) ).
thf(407,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_319942042_below @ A @ C @ B ) ) @ arrow_1985332922le_Lin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_prod_Orecs) ).
thf(566,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_PairE) ).
thf(461,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_prod__cases5) ).
thf(493,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_curryI) ).
thf(551,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
=> ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( pp @ ( aa @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TB @ TA ) ) @ D ) @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) ) )
=> ( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TB @ TA @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_funcset__mem) ).
thf(456,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( pp @ ( aa @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TB @ TA ) ) @ D ) @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) ) )
=> ( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ A ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TB @ TA @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(471,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(83,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_UNIV__I) ).
thf(488,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(124,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fFalse @ B @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(79,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(476,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Pair__inject) ).
thf(526,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(62,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_all__not__in__conv) ).
thf(393,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( product_curry @ TB @ TA @ TC @ C @ B @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_curry__conv) ).
thf(515,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( product_curry @ TB @ TA @ TC @ C @ B @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(108,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_iso__tuple__UNIV__I) ).
thf(569,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(118,axiom,
arrow_1958449194le_IIA @ f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I3_J) ).
thf(605,plain,
arrow_1958449194le_IIA @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(32,axiom,
arrow_2069624013nimity @ f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_u) ).
thf(237,plain,
arrow_2069624013nimity @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(58,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(360,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_prod__cases6) ).
thf(586,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(90,axiom,
( arrow_610318064e_Prof
= ( pi @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ arrow_159774573e_indi @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Prof__def) ).
thf(513,plain,
( arrow_610318064e_Prof
= ( pi @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( top_top @ ( fun @ arrow_159774573e_indi @ bool ) ) @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ arrow_159774573e_indi @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(19,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_424895264_mktop @ B @ A ) ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_mktop__Lin) ).
thf(166,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( arrow_424895264_mktop @ B @ A ) ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(148,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(43,axiom,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_987702531ctator @ B @ A )
<=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_dictator__def) ).
thf(264,plain,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_987702531ctator @ B @ A )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) )
& ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_split__paired__All) ).
thf(573,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_curryE) ).
thf(391,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
( ! [D: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TB @ TA @ B @ D ) ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TB @ TA ) ) @ B ) @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_funcsetI) ).
thf(313,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
( ! [D: TB] :
( ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TB @ TA @ B @ D ) ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TB @ TA ) @ ( fun @ ( fun @ ( fun @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TB @ TA ) ) @ B ) @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(87,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(498,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(36,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(245,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_prod__cases3) ).
thf(303,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(29,axiom,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ q ) @ arrow_610318064e_Prof ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096Q_A_058_AProf_096) ).
thf(208,plain,
pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ q ) @ arrow_610318064e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(116,axiom,
! [A: arrow_159774573e_indi] :
( ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ q @ A )
= ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ b1 ) @ b ) @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ a1 ) @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ ( arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ a @ a1 ) ) @ ( arrow_1158827142_above @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ a1 ) @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ ( arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ a @ a1 ) ) @ b1 @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Q__def) ).
thf(599,plain,
! [A: arrow_159774573e_indi] :
( ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ q @ A )
= ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ b1 ) @ b ) @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ a1 ) @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ ( arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ a @ a1 ) ) @ ( arrow_1158827142_above @ ( if @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ bool @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ bool ) @ ( fequal @ arrow_411405190le_alt ) @ a1 ) @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ ( arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) @ a @ a1 ) ) @ b1 @ b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(60,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_1958449194le_IIA @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_IIA__def) ).
thf(367,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_1958449194le_IIA @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ arrow_610318064e_Prof ) )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) ) )
=> ( arrow_1958449194le_IIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(56,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_1158827142_above @ C @ E @ D ) ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_in__above) ).
thf(323,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_1158827142_above @ C @ E @ D ) ) )
=> ( ( B != A )
& ( ( B = D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_1158827142_above @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(115,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_empty__Collect__eq) ).
thf(594,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(93,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( irrefl @ TA @ A )
<=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_irrefl__def) ).
thf(520,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ( ( irrefl @ TA @ A )
=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) ) @ A ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) ) @ A ) )
=> ( irrefl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( converse @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_converse__converse) ).
thf(130,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( converse @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( product_Pair @ TD @ TE ) @ F ) @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_prod__induct5) ).
thf(399,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( product_Pair @ TD @ TE ) @ F ) @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_in__inv__imagep) ).
thf(306,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) )
=> ( inv_imagep @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_split__paired__Ex) ).
thf(299,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( product_Pair @ TC @ TD ) @ E ) @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_prod__induct4) ).
thf(241,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( product_Pair @ TC @ TD ) @ E ) @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TB,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TB @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combc @ TA @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) @ TA @ ( combc @ TB @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ TA @ ( combb @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ TB @ ( member @ ( product_prod @ TA @ TB ) ) ) ) @ ( product_Pair @ TA @ TB ) ) ) ) @ A ) ) @ B ) @ C ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) @ ( converse @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_conversep__converse__eq) ).
thf(490,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: TB,C: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TB @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combc @ TA @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) @ TA @ ( combc @ TB @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ TA @ ( combb @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ TB @ ( member @ ( product_prod @ TA @ TB ) ) ) ) @ ( product_Pair @ TA @ TB ) ) ) ) @ A ) ) @ B ) @ C ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) @ ( converse @ TA @ TB @ A ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) @ ( converse @ TA @ TB @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TB @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( combc @ TA @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( fun @ TB @ bool ) ) @ TA @ ( combc @ TB @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) ) @ ( fun @ TA @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) ) @ ( combb @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( fun @ TB @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) ) @ TA @ ( combb @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ TB @ ( member @ ( product_prod @ TA @ TB ) ) ) ) @ ( product_Pair @ TA @ TB ) ) ) ) @ A ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_prod__cases4) ).
thf(589,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(97,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
& ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_complete__Lin) ).
thf(531,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
& ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(30,axiom,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) ) )
=> ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C ) ) ) ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_dictatorI) ).
thf(209,plain,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ B ) @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) ) )
=> ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ C ) @ arrow_610318064e_Prof ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ E ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C ) ) ) ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ B @ D ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Pi__I) ).
thf(553,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ B @ D ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool] :
( ( pi @ TA @ TB @ A @ ( combk @ ( fun @ TB @ bool ) @ TA @ ( top_top @ ( fun @ TB @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ TA @ TB ) @ bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Pi__UNIV) ).
thf(458,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool] :
( ( pi @ TA @ TB @ A @ ( combk @ ( fun @ TB @ bool ) @ TA @ ( top_top @ ( fun @ TB @ bool ) ) ) )
= ( top_top @ ( fun @ ( fun @ TA @ TB ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool )] :
( ( conversep @ TB @ TA @ ( conversep @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_conversep__conversep) ).
thf(145,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool )] :
( ( conversep @ TB @ TA @ ( conversep @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(95,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(525,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(69,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_319942042_below @ C @ E @ D ) ) )
<=> ( ( B != A )
& ( ( A = E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_in__below) ).
thf(414,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_319942042_below @ C @ E @ D ) ) )
=> ( ( B != A )
& ( ( A = E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( A = E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ ( arrow_319942042_below @ C @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(42,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(263,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(5,axiom,
b1 != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_d2_I2_J) ).
thf(127,plain,
b1 != a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ TB,D: fun @ TA @ bool] :
( ! [E: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ D ) )
=> ( ( aa @ TA @ TB @ C @ E )
= ( aa @ TA @ TB @ B @ E ) ) )
=> ( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ C ) @ ( pi @ TA @ TB @ D @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Pi__cong) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ TB,D: fun @ TA @ bool] :
( ! [E: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ D ) )
=> ( ( aa @ TA @ TB @ C @ E )
= ( aa @ TA @ TB @ B @ E ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ C ) @ ( pi @ TA @ TB @ D @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ D @ A ) ) ) )
& ( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ B ) @ ( pi @ TA @ TB @ D @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ C ) @ ( pi @ TA @ TB @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ D ) @ ( pi @ TA @ TB @ C @ B ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_PiE) ).
thf(177,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( pp @ ( aa @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ ( fun @ ( fun @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TB ) ) @ D ) @ ( pi @ TA @ TB @ C @ B ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ ( aa @ TA @ TB @ D @ A ) ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TB,D: TB] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TB ) @ ( fun @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TB ) ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) ) @ ( inv_image @ TA @ TB @ B @ A ) ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_in__inv__image) ).
thf(182,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TB,D: TB] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TB ) @ ( fun @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TB ) ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) ) @ ( inv_image @ TA @ TB @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) ) @ B ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TA ) @ ( fun @ ( fun @ ( product_prod @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TA ) ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) ) @ B ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TB ) @ ( fun @ ( fun @ ( product_prod @ TB @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TB ) ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) ) @ ( inv_image @ TA @ TB @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( total_on @ TA @ B @ ( converse @ TA @ TA @ A ) )
<=> ( total_on @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_total__on__converse) ).
thf(154,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
( ( ( total_on @ TA @ B @ ( converse @ TA @ TA @ A ) )
=> ( total_on @ TA @ B @ A ) )
& ( ( total_on @ TA @ B @ A )
=> ( total_on @ TA @ B @ ( converse @ TA @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_curryD) ).
thf(571,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_top__apply) ).
thf(250,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( top_top @ ( fun @ TB @ TA ) ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TB @ ( fun @ TB @ bool ),C: TA,D: TA] :
( ( inv_imagep @ TB @ TA @ B @ A @ C @ D )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_inv__imagep__def) ).
thf(556,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TB @ ( fun @ TB @ bool ),C: TA,D: TA] :
( ( ( inv_imagep @ TB @ TA @ B @ A @ C @ D )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ B @ ( aa @ TA @ TB @ A @ C ) ) @ ( aa @ TA @ TB @ A @ D ) ) )
=> ( inv_imagep @ TB @ TA @ B @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(99,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt @ A ) ) @ arrow_1985332922le_Lin ) )
<=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_converse__in__Lin) ).
thf(539,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt @ A ) ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) ) )
& ( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( converse @ arrow_411405190le_alt @ arrow_411405190le_alt @ A ) ) @ arrow_1985332922le_Lin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(54,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) )
=> ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Lin__irrefl) ).
thf(319,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) )
=> ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(40,axiom,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_top1I) ).
thf(258,plain,
! [TA: $tType,A: TA] : ( pp @ ( aa @ TA @ bool @ ( top_top @ ( fun @ TA @ bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(28,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_in__mkbot) ).
thf(186,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) )
=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) ) )
& ( ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_276188178_mkbot @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: product_prod @ TB @ TA] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ B ) @ ( converse @ TA @ TB @ A ) ) )
=> ~ ! [C: TA,D: TB] :
( ( B
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C ) )
=> ~ ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_converseE) ).
thf(401,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: product_prod @ TB @ TA] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TB @ TA ) ) @ B ) @ ( converse @ TA @ TB @ A ) ) )
=> ~ ! [C: TA,D: TB] :
( ( B
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C ) )
=> ~ ( pp @ ( aa @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ bool ) @ ( member @ ( product_prod @ TA @ TB ) ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_conversep__iff) ).
thf(171,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TB @ ( fun @ TA @ bool )] :
( ( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ A ) @ B ) )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( conversep @ TB @ TA @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(9,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(139,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(80,axiom,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_linear__alt) ).
thf(478,plain,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(536,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(13,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_d1_I2_J) ).
thf(151,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(67,axiom,
pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a1 ) @ b1 ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) ).
thf(410,plain,
pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ a1 ) @ b1 ) ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(20,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TA ) @ ( fun @ ( fun @ ( fun @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TA ) ) @ ( combi @ TA ) ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_funcset__id) ).
thf(168,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( pp @ ( aa @ ( fun @ ( fun @ TA @ TA ) @ bool ) @ bool @ ( aa @ ( fun @ TA @ TA ) @ ( fun @ ( fun @ ( fun @ TA @ TA ) @ bool ) @ bool ) @ ( member @ ( fun @ TA @ TA ) ) @ ( combi @ TA ) ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(65,axiom,
! [TA: $tType] :
? [A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_UNIV__witness) ).
thf(405,plain,
! [TA: $tType] :
? [A: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( top_top @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( combb @ TB @ TC @ TA @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(273,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( combb @ TB @ TC @ TA @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(106,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_emptyE) ).
thf(564,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(136,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ fTrue @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(358,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(78,axiom,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(474,plain,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(75,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( B != A )
=> ( ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) )
<=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_notin__Lin__iff) ).
thf(464,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C ) @ arrow_1985332922le_Lin ) )
=> ( ( B != A )
=> ( ( ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) ) )
& ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) ) @ C ) )
=> ~ ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(17,axiom,
pp @ ( aa @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ f ) @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_assms_I1_J) ).
thf(163,plain,
pp @ ( aa @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ f ) @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(501,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(82,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(486,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( fun @ TB @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TB @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_conversep_Ointros) ).
thf(469,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ TA @ ( fun @ TB @ bool )] :
( ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ C @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( conversep @ TA @ TB @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(50,axiom,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_UNIV__def) ).
thf(309,plain,
! [TA: $tType] :
( ( top_top @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fTrue ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(31,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_424895264_mktop @ B @ A ) ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_in__mktop) ).
thf(215,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_424895264_mktop @ B @ A ) ) )
=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) ) )
& ( ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( pp @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool @ ( aa @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ D ) @ C ) ) @ ( arrow_424895264_mktop @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( product_Pair @ TE @ TF ) @ G ) @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_prod__induct6) ).
thf(592,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( product_Pair @ TE @ TF ) @ G ) @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(59,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_UNIV__eq__I) ).
thf(364,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( top_top @ ( fun @ TA @ bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(86,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) ) @ arrow_610318064e_Prof ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_const__Lin__Prof) ).
thf(496,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( pp @ ( aa @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A ) @ arrow_1985332922le_Lin ) )
=> ( pp @ ( aa @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ) @ bool ) @ ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) ) @ arrow_610318064e_Prof ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(71,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_empty__iff) ).
thf(454,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(615,plain,
$false,
inference(cvc4,[status(thm)],[518,142,248,577,170,523,276,449,120,174,185,504,157,559,606,284,316,164,179,321,253,238,121,480,602,133,411,243,312,260,160,561,407,566,461,493,551,456,471,488,124,476,526,393,515,569,605,237,360,586,513,166,148,264,573,391,313,498,245,303,208,599,367,323,594,520,130,399,306,299,241,490,589,531,209,553,458,145,525,414,263,127,544,177,182,154,571,250,556,539,319,258,186,401,171,139,478,536,151,410,168,405,273,564,136,358,474,464,163,501,486,469,309,215,592,364,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT203_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 15:34:16 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.00 % [INFO] Parsing done (215ms).
% 1.36/1.00 % [INFO] Running in sequential loop mode.
% 2.31/1.21 % [INFO] eprover registered as external prover.
% 2.31/1.22 % [INFO] cvc4 registered as external prover.
% 2.31/1.22 % [INFO] Scanning for conjecture ...
% 2.77/1.35 % [INFO] Found a conjecture and 117 axioms. Running axiom selection ...
% 3.05/1.44 % [INFO] Axiom selection finished. Selected 117 axioms (removed 0 axioms).
% 3.82/1.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.82/1.65 % [INFO] Type checking passed.
% 3.82/1.65 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.36/1.79 % [INFO] [Domain constraints] Detected constraint on bool
% 4.36/1.79 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 4.48/1.84 % [INFO] [Domain constraints] Detected constraint on bool
% 4.48/1.84 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 262.43/205.51 % External prover 'cvc4' found a proof!
% 262.43/205.51 % [INFO] Killing All external provers ...
% 262.43/205.51 % Time passed: 205003ms (effective reasoning time: 204500ms)
% 262.43/205.51 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 262.43/205.51 % Axioms used in derivation (117): fact_11_d2_I1_J, fact_37_funcset__mem, fact_69_in__inv__image, fact_38_funcset__id, fact_84_conversep_Ointros, fact_97_empty__iff, fact_41_converseI, fact_39_dictator__def, fact_32_split__paired__All, fact_14_converse__in__Lin, fact_40_converseD, fact_65_curry__def, fact_64_curryE, fact_53_prod__induct5, fact_61_curry__conv, help_COMBI_1_1_U, fact_88_UNIV__def, fact_51_prod__cases6, fact_47_Pi__cong, fact_5_d1_I2_J, fact_17__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096, fact_94_Pi__empty, fact_45_prod_Orecs, fact_18_Q__def, fact_54_prod__cases4, help_fTrue_1_1_T, fact_30_PiE, fact_90_conversep_Osimps, fact_82_Pi__UNIV, fact_35_converse__converse, help_fNot_2_1_U, help_fTrue_1_1_U, fact_43_Pi__I, help_fNot_1_1_U, fact_66_total__on__converse, fact_87_iso__tuple__UNIV__I, fact_57_prod__cases3, fact_79_conversep__iff, fact_2_assms_I3_J, fact_71_inv__imagep__def, fact_56_prod__induct3, help_COMBB_1_1_U, fact_20_in__mkbot, fact_27_unanimity__def, help_If_1_1_T, fact_46_funcsetI, fact_26_converse__iff, fact_74_irrefl__def, fact_50_prod__induct6, fact_96_Collect__empty__eq, fact_42_converseE, fact_24_in__above, fact_9_above__Lin, fact_13_d1_I1_J, fact_95_emptyE, fact_83_conversepD, fact_19__C1_C, fact_63_curryD, arity_HOL_Obool___Orderings_Otop, fact_52_prod__cases5, fact_60_internal__split__conv, help_fequal_1_1_T, fact_76_mem__def, fact_0__096P_A_058_AProf_096, help_If_3_1_T, fact_15_notin__Lin__iff, fact_28_IIA__def, help_If_2_1_T, help_COMBK_1_1_U, fact_70_total__on__def, fact_6_mkbot__Lin, fact_36_Pi__mem, fact_31_complete__Lin, fact_93_Lin__def, fact_81_conversep__noteq, help_COMBC_1_1_U, fact_12_d2_I2_J, fact_8_assms_I1_J, fact_44_split__paired__Ex, help_fequal_2_1_T, fact_29_dictatorI, fact_85_conversep__conversep, fact_16__096P_H_A_058_AProf_096, fact_23_in__below, fact_55_prod__induct4, fact_34_Pair__inject, fact_80_conversep__eq, fact_86_UNIV__I, fact_3_u, fact_99_all__not__in__conv, fact_7_mktop__Lin, fact_10_below__Lin, fact_77_Collect__def, fact_4_linear__alt, fact_33_Pair__eq, fact_49_pred__equals__eq2, help_pp_1_1_U, fact_89_top__apply, fact_48_Pi__I_H, fact_78_top1I, fact_68_in__inv__imagep, fact_75_ext, fact_91_UNIV__eq__I, fact_22_const__Lin__Prof, arity_fun___Orderings_Otop, help_pp_2_1_U, fact_1__096Q_A_058_AProf_096, fact_58_PairE, fact_59_prod_Oexhaust, fact_25_Lin__irrefl, fact_92_UNIV__witness, fact_72_Prof__def, fact_73_conversep__converse__eq, fact_21_in__mktop, fact_98_empty__Collect__eq, fact_62_curryI, fact_67_converse__inv__image
% 262.43/205.51 % No. of inferences in proof: 238
% 262.43/205.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 205003 ms resp. 204500 ms w/o parsing
% 263.06/205.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 263.06/205.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------